Chapter 1

Question 1

Definition of a function

Answer 1

a function f from a set A to a set B is a relations that assigns to each element x in the set A exactly one element y in the set B. The set A is the domain of the function and the set B is the range of the function

Question 2

What are the 4 ways to represent a function?

Answer 2

verbally, numerically, graphically, algebraically

Question 3

The set of all numbers where the function is defined is called the domain. What are the two main ways functions are undefined?

Answer 3

when the denominator equals zero or an even root contains a negative value inside

Question 4

difference quotient

Answer 4

f(x+h) - f(x) / h

Question 5

slope intercept form

Answer 5

y = mx + b

Question 6

slope

Answer 6

rise/run = y2-y1/x2-x1

Question 7

point slope form

Answer 7

y - y1 = m (x-x1)

Question 8

parallel lines, slopes are ___

Answer 8

same

Question 9

perpendicular lines, slopes are____

Answer 9

negative reciprocals

Question 10

distance formula

Answer 10

the square root of (x2-x1)^2 + (y2-y1)^2

Question 11

midpoint formula

Answer 11

(x1+x2)/2, (y1+y2)/2

Question 12

equation of a circle

Answer 12

(x-h)^2 + (y-k)^2 = r^2

Question 13

how to find x intercept

Answer 13

let y=0, solve for x

Question 14

how to find y intercept

Answer 14

let x=0, solve for y

Question 15

how to test for x-axis symmetry

Answer 15

plug in “-y” for y and see if same

Question 16

how to test for y-axis symmetry

Answer 16

plug in “-x” for x and see if same

Question 17

how to test for origin symmetry

Answer 17

plug in “-x” for x and “-y” for y and see if same

Question 18

find zeros of a function

Answer 18

let f(x) = 0

Question 19

how to find rate of change

Answer 19

it is the same as slope

Question 20

how to test for even function

Answer 20

plug “-x” into f(x)

Question 21

how to test for odd function

Answer 21

plug “-x” into f(x)

Question 22

even functions are symmetric to _____

Answer 22

y axis

Question 23

odd functions are symmetric to _____

Answer 23

the origin

Question 24

f o g

Answer 24

f(g(x))

Question 25

g o f

Answer 25

g(f(x))

Question 26

g o g

Answer 26

g(g(x))

Question 27

how to verify that 2 functions are inverses

Answer 27

show that f(f^-1(x)) - x AND f^-1(f(x)) = x, therefore (3 dots) f and f^-1 are inverses